Silica-Based Particles, Method of Producing the Same, Paint for Forming Coating Film and Coated

ABSTRACT

To provide silica-based particles with a low refractive index, the hollow and spherical silica-based particles include porous materials or cavities inside an outer shell thereof by growing porous composite oxide particles (primary particles) adjusting a ratio of a quantity of added silica sources versus a quantity of added sources for an inorganic oxide other than silica and then removing the inorganic oxide other than silica. The dispersion liquid of silica-based particles is aged at a range from the room temperature to 300° C., cleaning is performed according to the necessity, and hydrothermal processing is performed at a temperature in the range from 50 to 300° C.

TECHNICAL FIELD

The present invention relates to silica-based particles having porousmaterials and/or cavities inside thereof, a method of producing thesilica-based particles, a paint for forming a coating film containingthe silica-based particles, and a coated substrate with the coating filmcontaining silica-based particles formed on a surface thereof.

BACKGROUND TECHNOLOGY

Hollow silica particles having a particle diameter in the range from 0.1to about 300 μm are known (Refer to, for instance, Patent document 1,and Patent document 2). Also there is known a method of producing hollowparticles each having a tight silica shell by depositing active silicafrom an aqueous solution of an alkali metal silicate on a core made of amaterial other than silica, and removing the material without breakingthe silica shell (Refer to, for instance, Patent document 3).

Furthermore, there is known spherical silica particles with the size atthe level of micron having a core shell structure comprising a shell inthe out peripheral portion and a hollow central portion. The shell has aconcentration gradient tighter toward the outer side and rougher towardthe inner side (Refer to, for instance, Patent document 4).

The present applicant already proposed to produce composite oxideparticles with the size at the nanometer level and also having a lowrefractive index by completely covering surfaces of porous inorganicoxide particles with such a material as silica (Refer to Patent Document5), and furthermore proposed to produce hollow silica-based particleswith the size at the nanometer level and also having a low refractiveindex by forming a silica coating layer on a particle of composite oxideincluding silica and an inorganic oxide other than silica, then removingthe inorganic oxide other than silica, and covering the particles withsilica, if necessary (Refer to Patent document 6).

However, with the particles proposed by the applicant, sometimes asufficiently low refractive index can not be obtained in practical useof the particles in some applications. Furthermore, in the method ofproducing the particles described in Patent document 6, the process israther complicated because of, for instance, the necessity of forming asilica coating layer prior to removal of the inorganic oxide other thansilica, and there are some problems in the reproducibility andproductivity.

Furthermore, in the conventional types of particles as described above,dispersibility of particles in the paint for forming a coating film usedin production of a coated substrate and stability of the paint are notsufficient, and a coating film obtained by using the paint for forming acoating film is sometimes not uniform in the thickness and notsufficient in the film strength. Furthermore, water adsorption causeswhite turbidity in the coating film, namely water resistance of thecoating film is sometimes insufficient.

Patent document 1: JP 06330606 A

Patent document 2: JP 07013137 A

Patent document 3: JP 2000500113 A

Patent document 4: JP 11029318 A

Patent document 5: JP 07133105 A

Patent document 6: JP 2001233611 A

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

The present invention is based on and an extension of the inventiondisclosed in Patent document 6, and an object of the present inventionis to provide silica-based particles with a low refractive index. Morespecifically an object of the present invention is to provide hollow andspherical silica-based particles including porous materials or cavitiesinside an outer shell thereof by growing porous composite oxideparticles (primary particles) adjusting a ratio of a quantity of addedsilica sources versus a quantity of added sources for an inorganic oxideother than silica and then removing the inorganic oxide other thansilica and a method of producing the silica-based particles.

Another object of the present invention is to provide a paint forforming a coating film containing the silica-based particles havingporous materials and/or cavities inside thereof and a matrix for forminga coating film and excellent in the stability and capability for forminga coating film.

Still another object of the present invention is to provide a coatedsubstrate having a low refractive index and excellent in adhesiveness toresin or the like as well as in the strength, capability of preventingreflection, and waterproof property.

Means for Solving the Problems

The method of producing silica-based particles according to the presentinvention includes the following steps (a), (b), (c) and (e):

(a) a step in which, when a dispersion liquid of composite oxideparticles is prepared by simultaneously adding an aqueous silicatesolution and/or an acidic silicic acid solution and an aqueous solutionof an alkali-soluble inorganic compound in an alkali aqueous solution orin an alkali aqueous solution with seed particles dispersed therein, ifrequired, the aqueous silicate solution and/or the acidic silicic acidsolution and the aqueous solution of alkali-soluble inorganic compoundare added so that the molar ratio of MO_(x)/SiO₂ are in a range from0.01 to 2, herein MO_(x) denoting an inorganic oxide other than silicaand SiO₂ denoting silica to prepare the dispersion liquid of compositeoxide particles with an average diameter (D_(p1)) in a range from 3 to300 nm,

(b) a step in which the aqueous silicate solution and/or the acidicsilicic acid solution and the aqueous solution of alkali-solubleinorganic compound are added at the molar ratio MO_(x)/SiO₂ smaller thanthat employed in the step (a) above to prepare a dispersion liquid ofthe composite oxide particles with the average diameters (D_(p2)) of upto 500 nm,

(c) a step in which an acid is added to the dispersion liquid ofcomposite oxide particles and then at least a portion of elementsconstituting the composite oxide particles other than silicon is removedto prepare a dispersion liquid of silica-based particles, and

(e) a step in which cleaning is performed according to the necessity,and the dispersion liquid of silica-based particles is aged at a rangefrom the room temperature to 300° C.

A value of B/A (A: the molar ratio MO_(x)/SiO₂ in step (a), B: the molarratio MO_(x)/SiO₂ in step (b)) is preferably 0.8 or below.

A ratio (D_(p1)/D_(p2)) of the average diameter (D_(p1)) of thecomposite oxide particles versus the average diameter (D_(p2)) of thecomposite oxide particles is preferably in the range from 0.4 to 0.98.

The step (b) and/or the step (c) above are preferably performed in thepresence of an electrolytic salt at a molar ratio (M_(E)/M_(S)) of 10 orbelow in which M_(E) denotes a mole number of the electrolytic salt andM_(S) denotes a mole number of SiO₂.

The following step (d) is preferably performed between the step (c) andthe step (e).

(d) a step in which an organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (c)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1)wherein R denotes a not-substituted or substituted hydrocarbon grouphaving 1 to 10 carbon atoms, an acrylic group, an epoxy group, amethacrylic group, amino group, or a CF₂ group; X denotes an alkoxygroup having 1 to 4 carbon atoms, a silanol group, a halogen orhydrogen; and n indicates an integral number in the range from 0 to 3.

Preferably the following step (f) is performed after the step (e).

(f) a step in which an organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (e)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1)wherein R denotes a not-substituted or substituted hydrocarbon grouphaving 1 to 10 carbon atoms, an acrylic group, an epoxy group, amethacrylic group, amino group, or a CF₂ group; X denotes an alkoxygroup having 1 to 4 carbon atoms, a silanol group, a halogen orhydrogen; and n indicates an integral number in the range from 0 to 3.

pH of the alkali aqueous solution or the alkali aqueous solution withseed particles dispersed therein according to the necessity, ispreferably 10 or more.

Preferably the following step (g) is performed after the step (e) orstep (f) above.

(g) a step in which cleaning is performed according to the necessity,and hydrothermal processing is performed at a temperature in the rangefrom 50 to 300° C.

Preferably the following step (h) is performed after the step (g) above.

(h) a step in which the organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (g)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1)wherein R denotes a not-substituted or substituted hydrocarbon grouphaving 1 to 10 carbon atoms, an acrylic group, an epoxy group, amethacrylic group, amino group, or a CF₂ group; X denotes an alkoxygroup having 1 to 4 carbon atoms, a silanol group, a halogen orhydrogen; and n indicates an integral number in the range from 0 to 3.

The hydrothermal processing step is preferably repeated several times.

The inorganic material other than silica is preferably alumina.

The obtained dispersion liquid of silica-based particles is preferablycleaned, dried, and calcinated, if required.

An average diameter of the silica-based particles is preferably in therange from 5 nm to 500 nm.

A content of an alkali metal oxide in the silica-based particles or thedispersion liquid of silica-based particles is preferably 5 ppm or belowas expressed by a content of M₂O per silica-based particle (M: alkalimetal element).

A content of ammonia and/or ammonium ions in the silica-based particlesor the dispersion liquid of silica-based particles is preferably 1500ppm or below as expressed by a content of NH₃.

The silica-based particles according to the present invention have aporous material and/or cavities in an outer shell thereof, and a ratioof a specific surface area (S_(B)) of the particles measured by the BETmethod versus a specific surface area (S_(C)) expressed by the followingexpression (S_(B)/S_(C)) is preferably in the range from 1.1 to 5:S _(c)(m²/g)=6000/Dp(nm)*ρwherein Dp denotes an average diameter of the silica-based particles,and ρ indicates a density (g/ml).

An average diameter of the silica-based particles is preferably in therange from 5 to 500 nm.

A thickness of the outer shell is in the range from 0.5 to 20 nm.

A refractive index of the silica-based particles is in the range from1.15 to 1.38.

The paint for forming coating film according to the present inventionincludes the silica-based particles produced by the production methoddescribed above or any of the silica-based particles described above,and a matrix for forming a coating film. Furthermore the paint forforming coating film preferably includes oxide-based particles otherthan the silica-based particles.

In the coated substrate according to the present invention, a coatingfilm containing the silica-based particles produced by the productionmethod described above or any of the silica-based particles describedabove and a matrix for forming a coating film is formed singly or incombination of other coating film on a surface of the substrate.

EFFECTS OF THE INVENTION

With the present invention, when composite oxide particles comprisingsilica and an inorganic oxide other than silica are prepared, at first acomposite oxide having a high content of the inorganic oxide other thansilica (primary particles) is prepared, and then a composite oxidehaving a high content of silica (secondary particles) is prepared, asilica content in a surface layer of the particles is high, and thecomposite oxide particles can preserve the spherical surface in thefollowing step of removing unnecessary elements and are not broken.Because of the features, silica-based particles having an extremely lowrefractive index can be prepared through an extremely simple productionprocess. Furthermore the production reproducibility and productivity ofthe silica-based particles are excellent.

After the steps of removing unnecessary elements and aging, or after thesteps of removing unnecessary elements and forming a silica-coatinglayer or aging according to the necessity, the silica-based particlesare obtained by hydrothermal processing at a high temperature. Insilica-based particles obtained as described above, contents of alkalimetal oxide, ammonia, and the like are lowered, and the paint forforming a coating film with the silica-based particles blended thereinis highly stable and provides a coating film having high strength.

Even when the hydrothermal processing is not performed, in thesilica-based particles obtained by forming a silica-coating layer afterthe step of removing unnecessary elements or by forming a silica layerafter the steps of removing unnecessary elements and aging, the S/Scdescribed below is in a range from 1.1 to 5, and preferably in the rangefrom 1.2 to 3, and the silica-based particles described above is welland homogeneously dispersed in the paint for forming a coating film, andthe obtained paint is excellent in the stability, and a coating filmobtained by using the paint is excellent in the strength and also in thewater resistance.

In the paint for forming a coating film according to the presentinvention, contents of the alkali metal oxide and ammonia in thesilica-based particles blended therein are low, so that the paint isexcellent in the stability, and therefore the coating film obtained byusing the paint is excellent in the strength.

Furthermore, the coated substrate according to the present invention hasa low refractive index, and is excellent in such properties asadhesiveness to resin or the like, strength, transparency, andreflection preventing property.

BEST MODE FOR CARRYING OUT THE INVENTION

Preferable embodiments of the present invention are described below.

[Method of Producing Silica-Based Particles]

The method of producing silica-based particles according to the presentinvention comprises the following steps (a), (b), (c) and (e). Sometimesstep (d) is performed between step (c) and step (e), or step (g) isperformed after step (e). Furthermore sometimes step (f) is performedafter step (e).

Each step is described below.

(a) a step in which, when a dispersion liquid of composite oxideparticles is prepared by simultaneously adding an aqueous silicatesolution and/or an acidic silicic acid solution and an aqueous solutionof an alkali-soluble inorganic compound in an alkali aqueous solution orin an alkali aqueous solution with seed particles dispersed therein, ifrequired, the aqueous silicate solution and/or the acidic silicic acidsolution and the aqueous solution of alkali-soluble inorganic compoundare added so that the molar ratio of MO_(x)/SiO₂ are in a range from0.01 to 2, herein MO_(x) denoting an inorganic oxide other than silicaand SiO₂ denoting silica to prepare the dispersion liquid of compositeoxide particles with an average diameter (D_(p1)) in a range from 3 to300 nm.

(b) a step in which the aqueous silicate solution and/or the acidicsilicic acid solution and the aqueous solution of alkali-solubleinorganic compound are added at the molar ratio MO_(x)/SiO₂ smaller thanthat employed in the step (a) above to prepare a dispersion liquid ofthe composite oxide particles with the average diameters (D_(p2)) of upto 500 nm.

(c) a step in which an acid is added to the dispersion liquid ofcomposite oxide particles and then at least a portion of elementsconstituting the composite oxide particles other than silicon is removedto prepare a dispersion liquid of silica-based particles.

(d) a step in which an organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (c)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1)wherein R denotes a not-substituted or substituted hydrocarbon grouphaving 1 to 10 carbon atoms, an acrylic group, an epoxy group, amethacrylic group, amino group, or a CF₂ group; X denotes an alkoxygroup having 1 to 4 carbon atoms, a silanol group, a halogen orhydrogen; and n indicates an integral number in the range from 0 to 3.(e) a step in which cleaning is performed according to the necessity,and the dispersion liquid of silica-based particles is aged at a rangefrom the room temperature to 300° C.(f) a step in which an organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (e)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1)wherein R denotes a not-substituted or substituted hydrocarbon grouphaving 1 to 10 carbon atoms, an acrylic group, an epoxy group, amethacrylic group, amino group, or a CF₂ group; X denotes an alkoxygroup having 1 to 4 carbon atoms, a silanol group, a halogen orhydrogen; and n indicates an integral number in the range from 0 to 3.(g) a step in which cleaning is performed according to the necessity,and then hydrothermal processing is performed at a temperature in therange from 50 to 300° C.(h) a step in which the organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (g)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1)wherein R denotes a not-substituted or substituted hydrocarbon grouphaving 1 to 10 carbon atoms, an acrylic group, an epoxy group, amethacrylic group, amino group, or a CF₂ group; X denotes an alkoxygroup having 1 to 4 carbon atoms, a silanol group, a halogen orhydrogen; and n indicates an integral number in the range from 0 to 3.Step (a)

One or more silicates selected from the group consisting of an alkalimetal silicate, an ammonium silicate, and a silicate of an organic baseare preferably used as the silicate. There can be enlisted sodiumsilicate (water glass) or potassium silicate as the alkali metalsilicate, and quaternary ammonium salts such as tetraethyl ammoniumsalt, and amines such as monoethanol amine, diethanol amine, ortriethanol amine as the organic base. The ammonium silicate or thesilicate of organic base includes an alkaline solution prepared byadding ammonia, quaternary ammonium hydroxide, and an amine compound ina silicic acid solution.

As the acidic silicic acid solution, it is possible to use a silicicacid solution obtained, for instance, by processing the alkali silicateaqueous solution with a cation exchange resin for removing the alkalinecomponents, and an acidic silicic acid solution with pH in the rangefrom 2 to 4 and the SiO₂ concentration of about 7% or below by weight isespecially preferable.

As the inorganic oxide, there can be enlisted one or more of Al₂O₃,B₂O₃, TiO₂, ZrO₂, SnO₂, Ce₂O₃, P₂O₅, Sb₂O₃, MoO₃, ZnO₂, WO₃, and thelike. As inorganic composite oxides, there can be enlisted, forinstance, TiO₂—Al₂O₃ and TiO₂—ZrO₂.

As raw materials for the inorganic oxides as described above, it ispreferable to use an alkali-soluble inorganic compound, and it ispossible to enumerate alkali metal salts or alkali-earth salts of anoxoacid metal salt or an oxoacid non-metal salt, ammonium salts, andquarternary ammonium salts constituting the inorganic oxides. Morespecifically, it is preferable to use sodium aluminate, sodiumtetraborate, zirconyl ammonium carbonate, potassium antimonate,potassium stannate, sodium aluminosilicate, sodium molybdate, ceriumammonium nitrate, sodium phosphate and the like.

For preparing a dispersion liquid of composite oxide particles,previously each alkali aqueous solution of the inorganic compounds isprepared separately or a mixed aqueous solution is prepared, and theaqueous solution is gradually added in an alkali aqueous solution, andpreferably in the alkali aqueous solution with the pH of 10 or more withagitation according to a target mixing ratio of silica and the inorganicoxide other than silica. The addition may be performed eithercontinuously or intermittently, but preferably silica and the inorganicoxide other than silica are added at the same time.

A mixing ratio of a quantity of raw materials for silica added in thealkali aqueous solution and that of raw materials for the inorganicoxide compound as expressed by the molar ratio MO_(x)/SiO₂ (SiO₂denoting silica and MO_(x) denoting the inorganic oxide other thansilica) is preferably adjusted to the range from 0.01 to 2, and morepreferably to the range from 0.1 to 1.5, until the composite oxideparticles having the average diameter in the range from 3 to 300 nm andmore preferably in the range from 5 to 100 nm (referred to as primaryparticles below) are obtained. When the molar ratio is less than 0.01, acavity volume of the finally obtained silica-based particles is notlarger sufficiently. On the other hand, when the molar ratio is morethan 2, it is difficult to obtain spherical composite oxide particles,and even if the spherical composite oxide particles can be obtained, thespherical composite oxide particles are broken when elements other thansilicon are removed, and as a result, silica-based particles having aporous material and/or cavity inside thereof can not be obtained.Addition of the two materials may be performed adjusting the molar ratioso that the value becomes gradually smaller.

When the molar ratio is in the range from 0.01 to 2, the composite oxideparticles have a structure in which silicon atom and elements other thansilicon are alternately coupled to each other via an oxygen atom.Namely, in many cases a structure is generated in which oxygen atoms arebonded to 4 bonding sites of the silicon atom, and an element M otherthan silicon is bonded to each of the oxygen atoms. In this case, whenthe element M other than silicon is removed in the step (c) describedbelow, also silicon atoms can be removed as a silicate monomer orsilicate oligomer in association with the element M without breaking thespherical form of the composite oxide particles.

Even if the molar ratio is within the range defined above, when anaverage diameter of the composite oxide particles (primary particles) isless than 3 nm, a percentage of the shell in each silica-based particlefinally obtained becomes larger, and a cavity volume in the silica-basedparticles is not sufficiently large. Furthermore, when the averagediameter of the composite oxide particles (primary particles) is morethan 300 nm, elements M other than silicon can not sufficiently beremoved in the step (c), and a cavity volume in the silica-basedparticles does not become sufficiently larger, which makes it difficultto obtain particles with a low refractive index.

In the production method according to the present invention, when adispersion liquid of composite oxide particles is prepared, a dispersionliquid with seed particles dispersed therein may be used as a startingmaterial. In this case, any of inorganic oxides such as SiO₂, Al₂O₃,TiO₂, ZrO₂, SnO₂ and CeO₂ or composite oxides of the materials such as,for instance, SiO₂—Al₂O₃, TiO₂—Al₂O₃, TiO₂—ZrO₂, SiO₂—TiO₂, andSiO₂—TiO₂—Al₂O₃ may be used, and generally the material can be used as asol. The dispersion liquid of the seed particles as described above canbe prepared by any known method. For instance, the dispersion liquid canbe obtained by adding an acid or an alkali in a metal salt correspondingto any of the inorganic oxides, in a mixture of the metal salts, or in ametal alcoxide for hydrolysis and aging the mixture, if required.

The aqueous solution of the compound is added with agitation accordingto the similar procedure for adding the solution in the alkali aqueoussolution, in the alkali aqueous solution with the seed particlesdispersed therein, and more preferably in the alkali aqueous solutionwith the seed particles dispersed therein and with the pH or 10 or more.When the composite oxide particles are grown by using seed particles asdescribed above, control over the particle diameter of the grownparticles is easy, and particles having relatively uniform size can beobtained. A ratio of raw material for silica versus the inorganiccompound each added in the dispersion liquid of seed particles is thesame employed when adding the materials in the alkali aqueous solution.

The raw material for silica and that for the inorganic material havehigh solubility in the alkali side. However, when the two materials aremixed with each other in a pH zone of the high solubility, solubility ofoxoacid ions such as silicate ion and aluminate ion drops, and thecomposite products of the materials are segregated and grow to colloidalparticles, or are deposited to the seed particles to grown intoparticles.

When the dispersion liquid of composite oxide particles is prepared,also the organic silicon compound expressed by the chemical formula (1)described below and/or a hydrolyte thereof may be added as a rawmaterial for silica in the alkali aqueous solution.

As the organic silicon compounds, there can be enumerated the followingmaterials: tetramethoxysilane, tetraethoxysilane, tetraisopropoxysilane,methyl trimethoxysilane, dimethyl dimethoxysilane, phenyltrimethoxysilane, diphenyl dimethoxysilane, methyl trimethoxysilane,dimethyl diethoxysilane, phenyl triethoxysilane, diphenyldiethoxysilane, isobutyl trimethoxysilane, vinyl trimethoxysilane, vinyltriethoxysilane, vinyl-tris(β-methoxyethoxy)silane,3,3,3-trifluoropropyl trimethoxysilane, methyl-3,3,3-trifluoropropyldimethoxysilane, β-(3,4epoxycyclohexyl)ethyl trimethoxysilane,γ-glycidoxytripropyl trimethoxysilane, γ-glycidoxypropyl methyldiethoxysilane, γ-glycidoxypropyl triethoxysilane, γ-methacryloxypropylmethyl dimethoxysilane, γ-methacryloxypropyl trimethoxysilane,γ-methacryloxypropyl methyl diethoxysilane, γ-methacryloxypropyltriethoxysilane, N-β(aminoethyl) γ-aminopropyl methyl dimethoxysilane,N-β(aminoethyl) γ-aminopropyl trimethoxysilane, N-β(aminoethyl)γ-aminopropyl triethoxysilane, γ-aminopropyl trimethoxysilane,γ-aminopropyl triethoxysilane, N-phenyl-γ-aminopropyl trimethoxysilane,γ-mercaptopropyl trimethoxysilane, trimethyl silanole, methyltrichlorosilane, methyl dichlorosilane, dimethyl dichlorosilane,trimethyl chlorosilane, phenyl trichlorosilane, diphenyl dichlorosilane,vinyl trichlorosilane, trimethyl bromosilane, and diethylsilane, and thelike.

In the organic silicon compound, when n is in the range from 1 to 3, thehydrophilicity is low. Therefore, it is preferable to previouslyhydrolyze the compound so that the compound can homogeneously be mixedin the reaction system. Any known method may be employed for hydrolyzingthe compounds. When a hydroxide of an alkali metal, ammonia water, or abasic compound such as amine is used as a catalyst for hydrolysis, thebasic catalyst may be removed after the hydrolysis and the solution maybe converted to an acidic solution for use. When a hydrolyzed product isprepared by using an acidic catalyst such as an organic acid or aninorganic acid, the acidic catalyst is preferably removed, for instance,by ion exchange. Furthermore it is desirable to use the hydrolyzedproduct of the organic silicon compound in a form of an aqueoussolution. The term of aqueous solution as used herein means the statewhere the hydrolyzed product is transparent and does not have whiteturbidity as gel.

Step (b)

Then, the primary particles are grown by adding an aqueous silicatesolution and/or an acidic silicic acid solution and an aqueous solutionof alkali-soluble inorganic compound at a molar ratio MO_(x)/SiO₂smaller than that employed in the step (a) under the average diametersof the particles (D_(p2)) grows up to 500 nm. The addition may beperformed either continuously or intermittently like in the step (a),but the both materials are preferably added simultaneously. Furthermore,the addition may be performed by gradually making smaller the molarratio MO_(x)/SiO₂ in the step (b).

The ratio of the molar ratio MO_(x)/SiO₂ in the step (a) (A) versus thatin the step (b) (B) [B/A] is preferably 0.8 or below.

When the value B/A is 1 or more, a silica-rich shell can not begenerated, which makes it difficult to obtain spherical composite oxideparticles. Even if the spherical composite oxide particles can beobtained, the spherical composite oxide particles are broken in the stepof removing elements other than silicon in the step (c), and as a resultsilica-based particles having porous materials and/or cavities insidethereof can not be obtained.

When the value B/A is less than 1, the surface layer of the compositeoxide particles becomes silica-rich, which makes it easier to form ashell, and even when elements other than silicon are removed in the step(c), the spherical composite oxide particles are not broken, which makesit possible to obtain silica-based particles having porous materialsand/or cavities inside thereof in stable state.

A ratio (Dp₁/D_(p2)) of average diameter (D_(p1)) of the composite oxideparticles versus average diameter (D_(p2)) of particles (secondaryparticles) obtained by growing the particles above is preferably in therange from 0.4 to 0.98, and more preferably in the range from 0.5 to0.96.

When the value of D_(p1)/D_(p2) is less than 0.4, the elements M otherthan silicon can not be removed sufficiently in the step (c) and thecavity volume in the silica-based particles does not become sufficientlylarger, which makes it difficult to obtain particles having a lowrefractive index. When the value of D_(p1)/D_(p2) is more than 0.98,sometimes silica-based particles having porous materials and/or cavitiescan not be obtained according to diameter of particles (morespecifically, when D_(p2) is 20 nm or below, and especially 10 nm orbelow).

In the present invention, in the step (b), after the average diameter ofthe composite oxide particles (primary particles) substantially grows upto the range from 3 to 300 nm, an electrolytic salt may be added at aratio of a mole number of the electrolytic salt (M_(E)) versus that ofSiO₂ (M_(S)) [M_(E)/M_(S)] in the range from 0.1 to 10 and morepreferably in the range from 0.2 to 8.

As the electrolytic salt, there can be enumerated water-soluble onessuch as sodium chloride, potassium chloride, sodium nitrate, potassiumnitrate, sodium sulfate, potassium sulfate, ammonium nitrate, ammoniumsulfate, magnesium chloride, and magnesium nitrate.

The electrolytic salt may be added all at once at this point of time, oradded continuously or intermittently adding an alkali metal silicate oran inorganic compound other than silica to grow composite oxideparticles.

Although a quantity of the electrolytic salt to be added changesaccording to a concentration of the dispersion liquid of the compositeoxide particles, when the molar ratio above (M_(E)/M_(S)) is less than0.1, the effect obtained by adding the electrolytic salt isinsufficient, and the composite oxide particles can not maintain thespherical form and are broken when an acid is added in the step (c) forremoving at least a portion of elements other than silicon constitutingthe composite oxide particles, which makes it difficult to obtainsilica-based particles having porous materials and/or cavities insidethereof. The effect obtained by adding the electrolytic salt ispresumably that silica content becomes higher at a surface of thecomposite oxide having grown into particles although the reason has notbeen clarified and the silica not soluble in an acid functions as aprotective film for the composite oxide particles.

Also when the molar ratio M_(S)/M_(E) is more than 10, the effectprovided by adding the electrolyte is not improved, and the economicalefficiency drops, for instance, because new fine particles aregenerated.

When the electrolytic salt is added, if the average diameter of theprimary particles is less than 3 nm, new fine particles grow, andselective growth of the primary particles does not occur, and sometimesdistribution of diameters of the composite oxide particles becomesheterogeneous. When the electrolytic salt is added, if the averagediameter of the primary particles is more than 300 nm, a long time isrequired for removing elements other than silicon in step (c), or eventhe process it self becomes difficult. The average diameter of thecomposite oxide particles (secondary particles) obtained as describedabove is, like the finally obtained silica-based particles, in the rangefrom 5 to 500 nm.

Step (c)

In step (c), a portion of or all of the elements other than silicon andconstituting the composite oxide particles are removed from thecomposite oxide particles.

The elements are removed from the composite oxide particles, forinstance, by adding a mineral acid or an organic acid to dissolve theelements for removal, by contacting the particles to a cation exchangeresin for ion exchange removal, or by combining the methods as describedabove.

Also in step (c), the elements other than silicon may be removed, afterthe electrolytic salt is added as described above to adjust the molarratio M_(S)/M_(E) to the range from 0.1 to 10, and more preferably tothe range from 0.2 to 8, by adding the mineral acid or the organic acidto dissolve the elements for removal, by contacting the particles to thecation exchange resin for ion exchange removal, or by combining themethods as described above.

A concentration of the dispersion liquid of composite oxide particles ispreferably in the range from 0.1 to 50 wt %, and more preferably in therange from 0.5 to 25 wt % when calculated as that of the oxide, althoughthe desirable concentration varies according to the processingtemperature. When the concentration of the composite oxide particles isless than 0.1 wt %, a quantity of dissolved silica increases, whichsometimes makes it difficult for the composite oxide particles tomaintain the form, and even when the composite oxide particles canmaintain the form, the concentration becomes lower, which lowers theprocessing efficiency. When the concentration of the composite oxideparticles is over 50 wt %, the particles are not dispersed sufficiently,which sometimes makes it difficult to uniformly or efficiently removeelements other than silica at fewer times from the composite oxideparticles having a high content of the elements other than silica.

Removal of the elements other than silica is preferably continues untilthe MO_(x)/SiO₂ in the obtained silica-based particles is in the rangefrom 0.0001 to 0.2, and more preferably in the range from 0.0001 to 0.1.

Step (d)

Step (d) is optional.

As the organic silicon compound expressed by the chemical formula (1),the organic silicon compounds as those used in step (a) may be used, andwhen the organic silicon compound expressed by the chemical formula (1)in which n is equal to 0 (n=0), it is preferable to use a partiallyhydrolyzed product of the organic silicon compound like that used in thestep (a) above.

Because the silica-coating layer as described above is condensed, theinside is preserved in a gas phase or in a liquid phase with a lowrefractive index, and when used for forming a coating layer, intrusionof a material with a high refractive index such as resin for paintinginto the inside is prevented, and a coating film with a low refractiveindex can be formed.

Furthermore, because the silica-coating layer is condensed, even whenthere is the gas phase portion inside thereof, water molecules do not gointo the inside. Namely the silica-coating layer has high waterresistance and can prevent the coating film from becoming turbid andwhite.

Because the silica-coating layer is condensed, a ratio (S_(B)/S_(c)) ofan actually measured specific surface area (S_(B)) of the silica-basedparticles versus a specific surface area (S_(c)) calculated from theaverage diameter is small, and conceivably because surface activity ofthe silica-based particles is low, dispersibility of the silica-basedparticles in a resin for a paint is high, and the obtained paint isexcellent in the stability.

When the organic silicon compound with n of 1 to 3 is used for forming asilica-coating layer, the dispersibility in an organic solvent is high,and a dispersion liquid of silica-based particles with high affinity toresin can be obtained. Furthermore, the surface may be processed, forinstance, with a silane coupling agent, but because the dispersibilityin an organic solvent and the affinity with resin are high, theprocessing may be omitted.

When an organic silicon compound containing fluorine is used for forminga silica-coating layer, a coating layer containing fluorine atoms isformed, so that the obtained particles has lower refractive index andthe dispersibility in an organic solvent is high, and therefore it ispossible to obtain a dispersion liquid of silica-based particles havinghigh affinity with resin. As the organic silicon compound containingfluoride, there can be enumerated 3,3,3-trifluoropropyltrimethoxysilane, methyl-3,3,3-trifluoropropyl dimethoxysilane,heptadecafluorodecyl trichlorosilane, heptadecafluorodecyltrichlorosilane, heptadecafluorodecyl trimethoxysilane, trifluoropropyltrimethoxysilane, tridecafluorooctyl trimethoxysilane, and the like.Furthermore also the compounds expressed by the chemical formula (2) orthe chemical formula (3) provide the same effect, and therefore thecompounds may advantageously be used for the purpose.

In the chemical formulas (2) and (3), R¹ and R², and R¹ and R⁷ may beidentical to or different from each other respectively, and denote anyof an alkyl group, a halogenated alkyl group, an aryl group, an alkylaryl group, an aryl alkyl group, an alkenyl group, a hydrogen atom, or ahalogen atom.

R³ to R⁶ may be identical to or different from each other, and denotesany of an alkoxy group, an alkyl group, a halogenated alkyl group, anaryl group, an alkyl aryl group, an aryl alkyl aryl group, an alkenylgroup, a hydrogen atom, or a halogen atom.

X denotes —C(C_(a)H_(b)F_(c))—, and a is a even integral number of 2 ormore, and b and c are even integral numbers of 0 or more.

Methoxysilane expressed as (CH₃O)₃SiC₂H₄C₆F₁₂C₂H₄Si(CH₃O)₃ is, forinstance, one of the compounds expressed by the chemical formula (2).

Step (e)

In step (e), the dispersion liquid of silica-based particles issubjected to cleaning, if required, and then is aged at a temperaturefrom the temperature to 300° C.

The dispersion liquid, from which the elements have been removed, can becleaned by any known method such as ultrafiltration according to thenecessity. A portion of the elements other than silicon dissolved in thedispersion liquid during cleaning are removed. In this step, if thedispersion liquid is subjected to ultrafiltration after a portion ofalkali metal ions, alkali earth metal ions, ammonium ions and the likehas been removed, a sol in which silica-based particles having highstability in the dispersed state can be obtained.

A portion of the elements other than silicon dissolved in the dispersionliquid or a portion of the alkali metal ions, alkali earth metal ions,and ammonium ions dissolved therein can be removed also by contactingthe dispersion liquid with a cation exchange resin and/or an anionexchange resin. The cleaning step becomes more effective when thedispersion liquid is heated before cleaning.

By subjecting the dispersion liquid to cleaning, it is possible toeffectively reduce contents of alkali metal oxides and ammonia in thesilica-based particles obtained through the hydrothermal processing asdescribed above, and because of this feature, properties of the paintfor forming a coating film obtained by using the silica-based particlesdescribed later such as the stability and adaptability for forming afilm are improved, and the obtained coating film is excellent in thestrength.

Then the dispersion liquid is aged, generally for 1 to 24 hours, at atemperature in the range from the room temperature to 300° C., and morepreferably at a temperature in the range from 50 to 250° C. When agingis performed, the silica-coating layer becomes more dense and tight, andmaterials with a high refractive index can not come into the particlesas described above, which makes it possible to form a coating filmhaving a low refractive index.

Step (f)

The step (f) is optional, and content of the step (e) is the same asthat of the step (d) excluding the point that the step (f) is performedafter the step (e).

Step (g)

Step (g) is optional, and in this step, cleaning is performed accordingthe necessity, and then the hydrothermal processing is performed at atemperature in the range from 50 to 300° C. Like in step (e), any knownmethod can be employed for cleaning.

When the temperature employed for the hydrothermal processing is lessthan 50° C., contents of alkali metal oxides and/or ammonia in thefinally obtained silica-based particles or the dispersion liquid ofsilica-based particles can not effectively be reduced, and the effectsfor improving the properties such as stability and adaptability toforming a coating film becomes insufficient, and also improvement in thestrength of obtained coating films is insufficient.

When the temperature employed for the hydrothermal processing is over300° C., properties of the paint for forming a coating film such as thestability, adaptability to forming a coating film, and strength are notfurther improved, and in some cases the silica-based particlesaggregate.

When the hydrothermal processing is performed at a temperature in therange from 150° C. to 300° C., a coating film obtained by using thesilica-based particles is excellent in the water resistance, and whendrops of water drop on the coating film, the water can easily be wipedoff. Also, when the drops of water are dried, trace of the water dropsis hardly left, which is advantageous.

In the present invention, the hydrothermal processing can be performedby repeating the step (g) described above. In this case, contents ofalkali metal oxide and/or ammonia in the silica-based particles or inthe dispersion liquid of the silica-based particles obtained byrepeating the step (g) can be reduced.

Step (h)

Step (h) is optional, and contents of the step (h) is the same as step(d) excluding the point that step (h) is performed after step (g).

A variation flow of the steps (c) and on is, for instance, as shownbelow.

Step (c): Removal of Elements

↓ → Step (d): Coating with silica

Step (e): Aging

↓ → Step (f): Coating with silica

Step (g): Hydrothermal Processing

↓ → Step (h): Coating with silica

An average diameter of the silica-based particles obtained as describedabove is in the range from 5 to 500 nm, and preferably in the range from10 to 400 nm. When the average diameter is less than 5 nm, a sufficientvolume of cavities can not be obtained, which makes it difficult toachieve the effect of lowering the refractive index. When the averagediameter is over 500 nm, it is difficult to obtain a stable dispersionliquid, and sometimes irregularities are generated on a surface of thecoating film containing the particles, and also the haze becomes higher.

An average diameter of the silica-based particles according to thepresent invention can be obtained by photographing the silica-basedparticles with a transmission electron microscope (TEM), measuringdiameter of 100 particles, and calculating the average value.

An average thickness of outer shell of the silica-based particles ispreferably in the range from 0.5 to 20 nm, and more preferably in therange from 1 to 15 nm. When a particle has an outer shell with thethickness of less than 0.5 nm, the particle can not maintain the form asa particle, so that it is difficult to obtain particles with thethickness of less than 0.5 nm. When the thickness is over 20 nm,percentages of porous materials and/or cavities inside the outer shellbecome lower, and therefore the particles can not provide the effect oflowering the refractive index.

Furthermore, a content of alkali metal oxides in the silica-basedparticles or a dispersion liquid of the silica-based particles ascalculated as that of M₂O (M: alkali metal element) per particle ispreferably 5 ppm or below, and more preferably 2 ppm or below. When thecontent of alkali metal oxides is over 5 ppm, stability of a paint forforming a coating film with the silica-based particles blended thereinis not sufficient. In this case, sometimes the viscosity becomes higher,the adaptability to forming a coating film drops with the strength of anobtained coating film lowered, and in addition the thickness of thecoating film may be not uniform.

Content of ammonia and/or ammonium ions in the silica-based particles orthe dispersion liquid of the silica-based particles when calculated asthat of NH₃ per silica-based particle is preferably 1500 ppm or below,and more preferably 1000 ppm or below. When the ammonia contents is over1500 ppm, like in the case where the content of the alkali metal oxideis too high, the viscosity becomes higher, the adaptability to forming acoating film drops with the strength of an obtained coating filmlowered, and in addition the thickness of the coating film may be notuniform.

In the method of producing silica-based particles according to thepresent invention, a sol of the silica-based particles dispersed in anorganic solvent can be obtained by substituting the obtained dispersionliquid of silica-based particles with an organic solvent by using anultrafiltration membrane, a rotary evaporator or the like.

The obtained silica-based particles may be processed with a silanecoupling agent by employing any known method.

Furthermore, in the method of producing silica-based particles accordingto the present invention, the silica-based particles can be cleaned, andthen dried and calcinated.

The silica-based particles obtained as described above have porousmaterials and/or cavities inside thereof and also have a low refractiveindex. Therefore, a coating film prepared by using the silica-basedparticles has a low refractive index, and is excellent in the reflectionpreventing property.

[Silica-Based Particles]

The silica-based particles according to the present invention haveporous materials and/or cavities inside an outer shell, and a ratio(S_(B)/S_(C)) of a specific surface area (S_(B)) of the particlesmeasured by the BET method versus a specific surface area (S_(C))expressed by the following expression is in a range from 1.1 to 5, andpreferably in the range from 1.2 to 3:S _(C)(m²/g)=6000/Dp(nm)*ρwherein Dp denotes an average diameter (nm) of the silica-basedparticles and p denotes a density (g/ml).

Herein the specific surface area (S_(B)) is a value obtained by heatingthe silica-based particles for 2 hours at 100° C. and then measuring thesurface area by the BET method (N₂ absorption method). On the otherhand, the specific surface area (S_(C)) is a value obtained bycalculation based on the assumptions that the silica-based particle isspherical and that a density ρ of the particle is 2.2 which isequivalent to a density of silica (g/ml), namely that the particle is anon-porous silica particle having a spherical form.

When the ratio (S_(B)/S_(C)) of the specific surface area (S_(B)) versusthe specific surface area (S_(C)) is less than 1.1, a pore volume or acavity volume in the porous material is small, and the effect oflowering the refractive index is not sufficient. On the other hand, whenthe ratio (S_(B)/S_(C)) is over 5, the outer shell become porous. Inthis case, dispersity of the particles in a resin for preparing a paintis not sufficient, and also stability of the obtained paint is notsufficient, which makes strength of a coating film prepared by using thesilica-based particles insufficient. Furthermore, sometimes watermolecules come into inside of the silica-based particles, which causeswhite turbidity in the coating film and furthermore makes the waterresistance of the coating film insufficient.

The ratio (S_(B)/S_(C)) is preferably in the range from 1.2 to 3.

An average diameter of silica-based particles according to the presentinvention is preferably in the range from 5 to 500 nm, and morepreferably in the range from 10 to 400 nm. When the average diameter isless than 5 nm, a percentage of the outer shell becomes higher, andsometimes the sufficient effect of lowering the refractive index can notbe obtained. When the average diameter is over 500 nm, it becomesdifficult to obtain a stable dispersion liquid or a stable paint, andirregularities may be generated on a surface of a coating filmcontaining the silica-based particles with the haze becoming moreremarkable. Furthermore an average diameter of the silica-basedparticles according to the present invention can be obtained byphotographing the silica-based particles with a transmission electronmicroscope (TEM), measuring diameters of 100 particles, and calculatingan average of the measured values.

An average thickness of the outer shells of the silica-based particlesis preferably in the range from 0.5 to 20 nm, and more specifically inthe range from 1 to 15 nm. When the thickness is less than 0.5 nm, theparticle can not maintain the spherical form, which makes it difficultto obtain the silica-based particles. When the thickness is over 20 nm,a percentage of the porous material and/or cavities inside the outershell becomes lower, which makes it difficult to provide the sufficienteffect of lowering the refractive index.

The average thickness of outer shells of the silica-based particles canbe obtained by measuring thicknesses of shell portions determinedaccording to a difference in contrast in the TEM image described aboveand calculating an average value from the measured values.

A refractive index of the silica-based particles is preferably in therange from 1.15 to 1.38, and more preferably in the range from 1.15 to1.35.

It is difficult to obtain silica-based particles with the refractiveindex of less than 1.15, and when the refractive index is over 1.38,sometimes a refractive index of the coating film prepared by using thesilica-based particles is over 1.42, and the reflection preventingproperty may be insufficient.

A refractive index of the silica-based particles is measured asdescribed below by using Series A, AA produced by CARGILL Corp. as astandard refractive liquid.

(1) A dispersion liquid of the silica-based particles is put in anevaporator to evaporate the dispersion medium.

(2) The dispersion liquid is dried at 120° C. to obtain powder.

(3) Two or three drops of a standard refractive liquid with a knownrefractive index are dropped on a glass plate, and the powder is mixedin the drops.

(4) The operation (3) above is performed in various types of standardrefractive liquids, and refractive indexes of the standard refractiveliquids when the mixture solutions become transparent are determined asrefractive indexes of the particles.

[Paint for Forming a Coating Film]

The paint for forming a coating film according to the present inventioncomprises the silica-based particles described above, a matrix forforming a coating film, and an organic solvent blended, if necessary.

The matrix for forming a coating film means a component capable offorming a coating film on a surface of the substrate and can be selectedand used from a resin or the like satisfying the conditions such asadhesiveness to a substrate, hardness, coating capability or the like.For instance, there can be enumerated a polyester resin, an acrylicresin, an urethane resin, a polyvinyl chloride resin, an epoxy resin, amelamine resin, a fluorine resin, a silicone resin, a butyral resin, aphenol resin, a vinyl acetate resin, an ultraviolet curing resin, anelectron beam curable resin, an emulsion resin, a water-soluble resin, ahydrophilic resin which has been conventionally used, a mixture of theresins and a resin such as a copolymer, variants thereof or the like, ora hydrolyzed organic silicon compounds such as the above-mentionedalkoxysilane or the like, and a partially hydrolyzed product thereof maybe used.

When a resin for paint is used as a matrix, for instance, the organicsolvent dispersion sol obtained by substituting the dispersion media ofthe silica-based particle dispersion liquid with an organic solvent suchas alcohol, preferably, the silica-based particles with a silica-coatinglayer formed by an organic silica compound containing an organic groupis used, and, the particles are processed by a known coupling agent, ifnecessary, before the organic solvent dispersion liquid blended in theorganic solvent and the resin for coating are diluted with a properorganic solvent to provide an coating liquid.

On the other hand, when a hydrolyzed organic silicon compound is used asa matrix, a partially hydrolyzed product of alkoxysilane is obtained byadding water, an acid or an alkali as a catalyst to the mixture solutionof alkoxysilane and alcohol, and the above-mentioned sol is addedthereto, and diluted with the organic solvent, if necessary, to obtainan coating liquid.

A weight ratio of the silica-based particle and the matrix in thecoating liquid for forming a coating film is preferably in the range ofthe silica-based particle/matrix from 1/99 to 9/1. When the weight ratioexceeds 9/1, the coating liquid lacks in practicality as the strength ofthe coating film and the adhesiveness with the substrate. On the otherhand, when the weight ratio is less than 1/99, addition of thesilica-based particle has an insufficient effect on lowering therefractive index of the coating film, increasing the adhesiveness withthe substrate, enhancing the strength of the coating film or the like.

[Substrate with a Coating Film]

In the substrate with a coating film according to the present invention,the coating film comprising the silica-based particles and the matrixfor forming a coating film is formed on a surface of the substratesingly or together with another coating film.

The substrate is a substrate with a coating film formed on the surfaceof glass, polycarbonate, an acryl resin, a PET, a plastic film such asTAC or the like, a plastic film, a plastic lens, a plastic panel or thelike, a cathode-ray tube, a fluorescent display, a LCD panel or thelike, and the coating film is formed singly or in combination with aprotective film, a hard coating film, a planarizing film, highrefractive index film, an insulating film, a conductive resin film, aconductive metal particle film, a conductive metal oxide particle filmand a primer film or the like used according to the necessity. It is tobe understood that the coating film according to the present inventiondoes not need to be formed on the outermost surface when the coatingfilm is used in combination with another film.

This kind of film can be obtained by applying the paint for forming acoating film described above to the substrate by a known method such asthe dipping method, the spray method, the spinner method, a roll coatingmethod or the like, drying, and additionally hardening by heating,exposing the film to ultraviolet radiation or the like, if necessary.

The refractive index of the coating film formed on the surface of theabove-mentioned substrate has a low refractive index from 1.15 to 1.42though the refractive index of the coating film varies according to theblend ratio of the silica-based particles, the matrix component or thelike and the refractive index of the matrix to be used. It is to beunderstood that the refractive index of the silica-based particlesaccording to the present invention is in the range from 1.15 to 1.38.The reasons are that the silica-based particles according to the presentinvention has porous materials and/or cavities inside thereof, and thatthe matrix-forming component such as a resin rests outside the particlesand therefore the cavities inside the silica-based particles aremaintained.

Furthermore, when the refractive index of the above-mentioned substratewith a coating film is 1.60 or less, the coating film including thesilica-based particles according to the present invention is recommendedto be formed after forming a coating film (hereinafter referred to as anintermediate film) with the refractive index of 1.60 or more on thesurface of the substrate. When the refractive index of the intermediatefilm is 1.60 or more, the difference from the refractive index of thecoating film including the above-mentioned silica-based particlesaccording to the present invention is large enough to obtain a substratewith a coating film excellent in the anti-reflection capability. Therefractive index of the intermediate film can be adjusted according tothe refractive index of the metal oxide particles used for improving therefractive index of the intermediate coating film, the mixing ratio ofthe metal oxide particle, the resin or the like, and the refractiveindex of the resin to be used.

The coating liquid for forming a coating film of the intermediate filmis a mixture of the metal oxide particle and the matrix for forming acoating film, and an organic solvent is mixed thereto, if necessary. Thesame matrix for forming a coating film as the one for forming a coatingfilm including the above-mentioned silica-based particle according tothe present invention may be used, and the substrate with a filmexcellent in adhesiveness between films can be obtained due to the usethe same matrix for forming a coating film.

The present invention is described more specifically below withreference to the embodiments.

EXAMPLE 1 Preparation of Silica-Based Particles (P-1)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 405 grams of aqueous solution of sodium silicatewith concentration of 1.5 wt % when calculated as that of SiO₂ and 405grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as that of Al₂O₃ were added to obtain a dispersionliquid of SiO₂.Al₂O₃ primary particles (average diameter: 28 nm). TheMO_(x)/SiO₂ molar ratio (A) then was 0.2, and the pH of the reactionliquid was 12.0. [Step (a)]

Next, 3250 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 1100 gramsof aqueous solution of sodium aluminate with concentration of 0.5 wt %when calculated as Al₂O₃ were added to obtain a dispersion liquid ofcomposite oxide particles (1) (secondary particles) (average diameter:40 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.07, and the pH of thereaction liquid was 12.0. [Step (b)]

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (1) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(P-1-1) with solid-phase concentration of 20 wt %. [Step (c)]

Next, mixed fluid of 150 grams of water dispersion liquid of thesilica-based particles (P-1-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 190 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-1-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-1-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-1-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-1-2) were 6 ppm and 1200 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-1-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-1-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-1-3) were 0.5 ppm and 800 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-1) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparation conditions of the silica-based particles (P-1) are given inTable 1. Table 2 shows the characteristics of the silica-based particles(P-1) such as an average diameter, thickness of an outer shell layer,MO_(x)/SiO₂ (molar ratio), Na₂O content, NH₃ content, a refractiveindex, specific surface area (S_(B)), specific surface area (S_(C)), andwater resistance of silica-based particles (P-1). The average diameterand the thickness of an outer shell layer were measured using the TEMmethod, and the refractive index was measured using Cargill's Series A,AA as a standard liquid having a known refractive index.

The water resistance was measured according to the following method.

Mixture solution of 5 grams of ortho-ethyl silicate (TEOS) (SiO₂content: 28 wt %), 19.5 grams of ethanol, 0.14 grams of condensed nitricacid, and 3.4 grams of pure water was agitated at the room temperaturefor 5 hours to prepare binder component of SiO₂ with concentration of 5wt %. 1.75 grams of alcohol dispersion liquid of silica-based particles(P-1) with solid content of 20 wt % was mixed, and was applied on aglass plate by the spin coat method and was dried at 120° C. for 5 hoursto form a transparent film. One drop of distilled water was dropped onthe transparent film and was wiped off. A mark of the drop was observedand evaluated according to the following criteria. No mark of the dropwas observed.: ⊚ The mark of the drop was observed but disappearedwithin ◯ 5 minutes.: The mark of the drop was disappeared in 5 to 20minutes.: Δ The mark of the drop was observed 20 minutes or more.: XPreparing a Substrate with a Transparent Coating Film (A-1)

50 grams of dispersion liquid of solid content of 5 wt % prepared bydiluting alcohol dispersion liquid of the silica-based particles (P-1)with ethanol, 3 grams of acrylic resin (Hitaloid 1007: Hitachi KaseiK.K.), and 47 grams of mixed solvent of iso-propanol and n-butanol atthe rate of 1/1 (weight ratio) were sufficiently mixed to prepare acoating liquid.

This coating liquid was applied on a PET film by the bar coater method,and was dried at 80° C. for 1 minute to obtain a substrate withtransparent coating film (A-1) with the thickness of 100 nm. Totaltransmittance, haze, reflectance for a light having 550 nm wavelength,refractive index of the film, adhesiveness, and pencil hardness of thesubstrate with transparent coating film (A-1) are shown in Table 3.

The total transmittance and the haze are measured by Haze Meter(manufactured by Suga Test Instruments Co., Ltd.) and the reflectance ismeasured by a spectrophotometer (Ubest-55 manufactured by JascoCorporation) respectively. Also, the refractive index of the coatingfilm is measured by an ellipsometer (EMS-1 manufactured by ULVAC Inc.).It is to be understood that the total transmittance of the unembrocatedPET film is 90.7%, haze thereof is 2.0%, and the reflectance for a lightwith the wavelength of 550 nm is 7.0%. The pencil hardness is measuredby a pencil hardness tester according to JIS K 5400. Namely, a pencil isset at an angle of 45 degrees with respect to a surface of the film,drawn at a constant velocity with a predetermined weight and observed ifthere is a blemish or not.

On a surface of the Substrate with a Transparent Coating Film (A-1), 100meshes were created by 11 parallel lines in both two directionssubstantially perpendicular to each other using a knife. A scotch tapewas stuck on the surface and the tape was removed. Then the number ofremaining meshes without the film being removed was counted to evaluatethe adhesiveness by categorizing in any of the following three stages.The results were shown in table 3. 90 or more pieces of meshes remained:⊚ 85-89 pieces of meshes remained: ◯ 84 or less pieces of meshesremained: Δ

EXAMPLE 2 Preparation of Silica-Based Particles (P-2)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 1750 grams of aqueous solution of sodium silicatewith concentration of 1.5 wt % when calculated as that of SiO₂ and 1750grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as that of Al₂O₃ were added to obtain a dispersionliquid of SiO₂.Al₂O₃ primary particles (average diameter: 35 nm). TheMO_(x)/SiO₂ molar ratio (A) then was 0.2, and the pH of the reactionliquid was 12.0. [Step (a)]

Next, 6300 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 2100 gramsof aqueous solution of sodium aluminate with concentration of 0.5 wt %when calculated as Al₂O₃ were added to obtain a dispersion liquid ofcomposite oxide particles (2) (secondary particles) (average diameter:50 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.07, and the pH of thereaction liquid was 12.0. [Step (b)]

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (2) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(P-2-1) with solid-phase concentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-2-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 140 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-2-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-2-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 200° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-2-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-2-2) were 8 ppm and 1500 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-2-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-2-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-2-3) were 0.4 ppm and 60 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-2) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-2)

A substrate with a transparent coating film (A-2) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-2) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 3 Preparation of Silica-Based Particles (P-3)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 109,800 grams of aqueous solution of sodiumsilicate with concentration of 1.5 wt % when calculated as that of SiO₂and 109,800 grams of aqueous solution of sodium aluminate withconcentration of 0.5 wt % when calculated as that of Al₂O₃ were added toobtain a dispersion liquid of SiO₂.Al₂O₃ primary particles (averagediameter: 120 nm). The MO_(x)/SiO₂ molar ratio (A) then was 0.2, and thepH of the reaction liquid was 12.0. [Step (a)]

Next, 251,700 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 83,900grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as Al₂O₃ were added to obtain a dispersion liquidof composite oxide particles (3) (secondary particles) (averagediameter: 171 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.07, andthe pH of the reaction liquid was 12.0. [Step (b)]

Next, 1125 grams of pure water was added to 500 grains of dispersionliquid of the composite oxide particles (3) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(P-3-1) with solid-phase concentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-3-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 33 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-3-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-3-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-3-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-3-2) were 10 ppm and 1200 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-3-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-3-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-3-3) were 0.4 ppm and 600 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-3) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-3)

A substrate with a transparent coating film (A-3) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-3) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 4 Preparation of Silica-Based Particles (P-4)

In the same method in example 2, the dispersion liquid of SiO₂.Al₂O₃primary particles (average diameter: 35 nm) with 20 wt % solid contentwas prepared. [Step (a)]

Next, 3300 grams of aqueous solution of sodium sulfate withconcentration of 1.5 wt % (molar ratio: 0.5) was added, and 6300 gramsof aqueous solution of sodium silicate with concentration of 1.5 wt %when calculated as that of SiO₂ and 2100 grams of aqueous solution ofsodium aluminate with concentration of 0.5 wt % when calculated as Al₂O₃were added to obtain a dispersion liquid of composite oxide particles(4) (secondary particles) (average diameter: 50 nm). The MO_(x)/SiO₂molar ratio (B) then was 0.15, and the pH of the reaction liquid was12.0. [Step (b)]

Next, 1125 grams of pure water and 100 grams of sodium sulfate withconcentration of 0.5 wt % (molar ratio: 0.004) were added to 500 gramsof dispersion liquid of the composite oxide particles (4) withsolid-phase concentration of 13 wt % after cleaned with anultrafiltration membrane. Drops of concentrated hydrochloric acid(concentration: 35.5 wt %) were added so as to set the pH to 1.0 to bedealuminated. Next, while 10 L of hydrochloric acid solution with pH3and 5 L of pure water were added, aluminate dissolved with theultrafiltration membrane was separated and cleaned to obtain an aqueousdispersion liquid of silica-based particles (P-4-1) with solid-phaseconcentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-4-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 140 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-4-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-4-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-4-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-4-2) were 7 ppm and 900 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-4-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-4-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-4-3) were 0.3 ppm and 700 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-4) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-4)

A substrate with a transparent coating film (A-4) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-4) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 5 Preparation of Silica-Based Particles (P-5)

In the same method in example 2, the dispersion liquid of SiO₂.Al₂O₃primary particles (average diameter: 35 nm) with 20 wt % solid contentwas prepared. [Step (a)]

Next, 6600 grams of aqueous solution of sodium sulfate withconcentration of 1.5 wt % (molar ratio: 1.0) was added, and 6300 gramsof aqueous solution of sodium silicate with concentration of 1.5 wt %when calculated as that of SiO₂ and 2100 grams of aqueous solution ofsodium aluminate with concentration of 0.5 wt % when calculated as Al₂O₃were added to obtain a dispersion liquid of composite oxide particles(5) (secondary particles) (average diameter: 50 nm). The MO_(x)/SiO₂molar ratio (B) then was 0.07, and the pH of the reaction liquid was11.0. [Step (b)]

Next, 1125 grams of pure water and 100 grams of sodium sulfate withconcentration of 0.5 wt % (molar ratio: 0.004) were added to 500 gramsof dispersion liquid of the composite oxide particles (5) withsolid-phase concentration of 13 wt % after cleaned with anultrafiltration membrane. Drops of concentrated hydrochloric acid(concentration: 35.5 wt %) were added so as to set the pH to 1.0 to bedealuminated. Next, while 10 L of hydrochloric acid solution with pH3and 5 L of pure water were added, aluminate dissolved with theultrafiltration membrane was separated and cleaned to obtain an aqueousdispersion liquid of silica-based particles (P-5-1) with solid-phaseconcentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-5-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 140 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-5-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-5-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-5-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-5-2) were 6 ppm and 1100 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-5-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-5-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-5-3) were 0.5 ppm and 600 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-5) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-5)

A substrate with a transparent coating film (A-5) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-5) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 6 Preparation of Silica-Based Particles (P-6)

In example 5, the dispersion liquid of silica-based particles (P-5-2)was cleaned with an ultrafiltration membrane while 5 L of pure water wasadded, without being processed hydrothermally at 150° C. for 11 hours,to obtain an aqueous dispersion liquid of silica-based particles (P-6-3)with solid content of 20 wt %. At that time, Na₂O and NH₃ content persilica-based particle in the dispersion liquid of silica-based particles(P-6-3) were 0.8 ppm and 1200 ppm respectively.

Next, an alcohol dispersion liquid of silica-based particles (P-6) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-6)

A substrate with a transparent coating film (A-6) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-6) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 7 Preparation of Silica-Based Particles (P-7)

In the same method in example 5, the dispersion liquid of primaryparticles was prepared, and 6600 grams of aqueous solution of sodiumsulfate with concentration of 0.5 wt % (molar ratio: 1.0) was added, andthen 6670 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 1050 gramsof aqueous solution of sodium aluminate with concentration of 0.5 wt %when calculated as Al₂O₃ were added to obtain a dispersion liquid ofcomposite oxide particles (7) (secondary particles) (average diameter:50 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.03, and the pH of thereaction liquid was 11.2. [Step (a), (b)]

Next, 1125 grams of pure water and 100 grams of sodium sulfate withconcentration of 0.5 wt % (molar ratio: 0.004) were added to 500 gramsof dispersion liquid of the composite oxide particles (7) withsolid-phase concentration of 13 wt % after cleaned with anultrafiltration membrane. Drops of concentrated hydrochloric acid(concentration: 35.5 wt %) were added so as to set the pH to 1.0 to bedealuminated. Next, while 10 L of hydrochloric acid solution with pH3and 5 L of pure water were added, aluminate dissolved with theultrafiltration membrane was separated and cleaned to obtain an aqueousdispersion liquid of silica-based particles (P-7-1) with solid-phaseconcentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-7-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 140 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-7-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-7-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-7-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-7-2) were 8 ppm and 1200 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-7-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-7-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-7-3) were 0.9 ppm and 700 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-7) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-7)

A substrate with a transparent coating film (A-7) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-7) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 8 Preparation of Silica-Based Particles (P-8)

In the same method in example 5, the aqueous dispersion liquid ofsilica-based particles (P-5-1) with solid-phase concentration of 20 wt%. [Step (c)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-5-1) to adjust the pH of the dispersion liquidto be 10.5. The dispersion liquid was aged at 150° C. for 11 hours,without forming silica coating layer, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-8-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-8-2) were 10 ppm and 1400 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-8-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-8-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-8-3) were 1.0 ppm and 700 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-8) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-8)

A substrate with a transparent coating film (A-8) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-8) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 9 Preparation of Silica-Based Particles (P-9)

In the same method in example 2, the dispersion liquid of SiO₂.Al₂O₃primary particles (average diameter: 35 nm) with 20 wt % solid contentwas prepared. [Step (a)]

Next, 6600 grams of aqueous solution of sodium sulfate withconcentration of 0.5 wt % (molar ratio: 1.0) was added, and 33,000 gramsof aqueous solution of sodium silicate with concentration of 1.5 wt %when calculated as that of SiO₂ and 11,000 grams of aqueous solution ofsodium aluminate with concentration of 0.5 wt % when calculated as Al₂O₃were added to obtain a dispersion liquid of composite oxide particles(9) (secondary particles) (average diameter: 78 nm). The MO_(x)/SiO₂molar ratio (B) then was 0.07, and the pH of the reaction liquid was11.0. [Step (b)]

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (9) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(P-9-1) with solid-phase concentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-9-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 80 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-9-1) having a silica-coating layer with solid content of 20wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-9-1) having the silica-coating layer to adjustthe pH of the dispersion liquid to be 10.5. Then, the dispersion liquidwas aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-9-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-9-2) were 2 ppm and 1500 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-9-2) wasprocessed hydrothermally at 150° C. for 11 hours and cooled to the roomtemperature. The dispersion liquid was ion-exchanged for 3 hours using400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-9-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-9-3) were 0.9 ppm and 800 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-9) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-9)

A substrate with a transparent coating film (A-9) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-9) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 10 Preparation of Silica-Based Particles (P-10)

In the same method in example 2, the dispersion liquid of SiO₂.Al₂O₃primary particles (average diameter: 35 nm) with 20 wt % solid contentwas prepared. [Step (a)]

Next, 6600 grams of aqueous solution of sodium sulfate withconcentration of 0.5 wt % (molar ratio: 1.0) was added, and 600 grams ofaqueous solution of sodium silicate with concentration of 1.5 wt % whencalculated as that of SiO₂ and 200 grams of aqueous solution of sodiumaluminate with concentration of 0.5 wt % when calculated as Al₂O₃ wereadded to obtain a dispersion liquid of composite oxide particles (10)(secondary particles) (average diameter: 37 nm). The MO_(x)/SiO₂ molarratio (B) then was 0.07, and the pH of the reaction liquid was 11.1.[Step (b)]

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (10) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(P-10-1) with solid-phase concentration of 20 wt %. [Step (c)]

Next, mixed liquid of 150 grams of water dispersion liquid of thesilica-based particles (P-10-1), 500 grams of pure water, 1750 grams ofethanol, and 626 grams of ammonia water with concentration of 28 wt %was heated to 35° C. Then, 208 grams of ethyl silicate (SiO₂concentration: 28 wt %) was added to form a silica-coating layer, andwas cleaned with an ultrafiltration membrane, while 5 L of pure waterwas added, to obtain an aqueous dispersion liquid of silica-basedparticles (P-10-1) having a silica-coating layer with solid content of20 wt %. [Step (d)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-10-1) having the silica-coating layer toadjust the pH of the dispersion liquid to be 10.5. Then, the dispersionliquid was aged at 150° C. for 11 hours, and was cooled to the roomtemperature. Then, the dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (P-10-1) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (P-10-1) were 8 ppm and 1000 ppm respectively.[Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-10-1)was processed hydrothermally at 150° C. for 11 hours and cooled to theroom temperature. The dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-10-1) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-10-1) were 0.8 ppm and 700 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-10) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-10)

A substrate with a transparent coating film (A-10) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-10) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 11 Preparation of Silica-Based Particles (P11)

A mixture of 100 grams of silica sol having an average diameter of 5 nmand 3900 grams of pure water were heated to 98° C. In this procedure, pHof mother liquid was 10.5. While this temperature was kept, 7000 gramsof aqueous solution of sodium silicate with concentration of 1.5 wt %when calculated as that of SiO₂ and 7000 grams of aqueous solution ofsodium aluminate with concentration of 0.5 wt % when calculated as thatof Al₂O₃ were added to obtain a dispersion liquid of SiO₂.Al₂O₃ primaryparticles (average diameter: 10 nm). The MO_(x)/SiO₂ molar ratio (A)then was 0.2, and the pH of the reaction liquid was 12.0. [Step (a)]

Next, 16,740 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 5,580grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as Al₂O₃ were added to obtain a dispersion liquidof composite oxide particles (11) (secondary particles) (averagediameter: 14 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.07, and thepH of the reaction liquid was 12.0. [Step (b)]

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (11) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(P-11-1) with solid-phase concentration of 20 wt %. [Step (c)]

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (P-11-1) to adjust the pH of the dispersionliquid to be 10.5. Then, the dispersion liquid was aged at 150° C. for11 hours, and was cooled to the room temperature. Then, the dispersionliquid was ion-exchanged for 3 hours using 400 grams of cation exchangeresin (Mitsubishi Kagaku K.K.: Diaion SK1B), and ion-exchanged for 3hours using 200 g of anion exchange resin (Mitsubishi Kagaku K.K.:Diaion SA20A), and ion-exchanged at 80° C. for 3 hours using 200 g ofcation exchange resin (Mitsubishi Kagaku K.K.: Diaion SK1B), to obtainan aqueous dispersion liquid of silica-based particles (P-11-2) of solidcontent of 20 wt %. At that time, Na₂O and NH₃ content per silica-basedparticle in the aqueous dispersion liquid of silica-based particles(P-11-2) were 8 ppm and 1000 ppm respectively. [Step (e)]

Next, again, the dispersion liquid of silica-based particles (P-11-2)was processed hydrothermally at 150° C. for 11 hours and cooled to theroom temperature. The dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (P-11-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (P-11-3) were 0.9 ppm and 1000 ppm respectively.[Step (g)]

Next, an alcohol dispersion liquid of silica-based particles (P-11) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (A-1)

A substrate with a transparent coating film (A-11) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-11) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

EXAMPLE 12 Preparation of Silica-Based Particles (P-12)

The alcoholic dispersion liquid of silica-based particles (P-8) having20 wt % of solid phase concentration was prepared by using the sameprocedure to Example 8. [Step (g)]

An alcoholic dispersion liquid of silica-based particles (P-12) having20 wt % of solid phase concentration and substituted solvent to ethanolwas prepared by adding 15 g of acrylsilane coupling agent (KBM-5103:produced by Shin-Etsu Chemical Co., Ltd.) to 100 g of the alcoholicdispersion liquid of silica-based particles (P-8), and heating at 50° C.and using again ultrafiltration membrane. [Step (h)]

Preparing a Substrate with a Transparent Coating Film (A-12)

A substrate with a transparent coating film (A-12) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (P-12) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

COMPARATIVE EXAMPLE 1 Preparation of Silica-Based Particles (RP-1)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 1750 grams of aqueous solution of sodium silicatewith concentration of 1.5 wt % when calculated as that of SiO₂ and 1750grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as that of Al₂O₃ were added to obtain a dispersionliquid of SiO₂.Al₂O₃ primary particles (average diameter: 35 nm). TheMO_(x)/SiO₂ molar ratio (A) then was 0.2, and the pH of the reactionliquid was 12.0.

Next, 5270 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 5270 gramsof aqueous solution of sodium aluminate with concentration of 0.5 wt %when calculated as Al₂O₃ were added to obtain a dispersion liquid ofcomposite oxide particles (R1) (secondary particles) (average diameter:50 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.2, and the pH of thereaction liquid was 12.0.

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (R1) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(RP-1) with solid-phase concentration of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (RP-1) were 1000 ppm and less than 10 ppmrespectively.

When the average diameter of the silica-based particles (RP-1) wasmeasured, it was approximately 5 nm. And when the silica-based particles(RP-1) were observed by taking transmission electron microscope (TEM),fine particles hardly have void. No substrate having transparent coatingfilm was manufactured.

COMPARATIVE EXAMPLE 2 Preparation of Silica-Based Particles (RP-2)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 2215 grams of aqueous solution of sodium silicatewith concentration of 1.5 wt % when calculated as that of SiO₂ and 350grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as that of Al₂O₃ were added to obtain a dispersionliquid of SiO₂.Al₂O₃ primary particles (average diameter: 35 nm). TheMO_(x)/SiO₂ molar ratio (A) then was 0.03, and the pH of the reactionliquid was 12.0.

Next, 6670 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 1055 gramsof aqueous solution of sodium aluminate with concentration of 0.5 wt %when calculated as Al₂O₃ were added to obtain a dispersion liquid ofcomposite oxide particles (RP2) (secondary particles) (average diameter:50 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.03, and the pH of thereaction liquid was 12.0.

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (RP2) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(RP-2-1) with solid-phase concentration of 20 wt %.

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (RP-2-1) to adjust the pH of the dispersionliquid to be 10.5. Then, the dispersion liquid was aged at 150° C. for11 hours, and was cooled to the room temperature. Then, the dispersionliquid was ion-exchanged for 3 hours using 400 grams of cation exchangeresin (Mitsubishi Kagaku K.K.: Diaion SK1B), and ion-exchanged for 3hours using 200 g of anion exchange resin (Mitsubishi Kagaku K.K.:Diaion SA20A), and ion-exchanged at 80° C. for 3 hours using 200 g ofcation exchange resin (Mitsubishi Kagaku K.K.: Diaion SK1B), to obtainan aqueous dispersion liquid of silica-based particles (RP-2-2) of solidcontent of 20 wt %. At that time, Na₂O and NH₃ content per silica-basedparticle in the aqueous dispersion liquid of silica-based particles(RP-2-2) were 6 ppm and 1500 ppm respectively.

Next, again, the dispersion liquid of silica-based particles (RP-2-2)was processed hydrothermally at 150° C. for 11 hours and cooled to theroom temperature. The dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (RP-2-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (RP-2-3) were 0.5 ppm and 900 ppm respectively.

Next, an alcohol dispersion liquid of silica-based particles (RP-2) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (RA-2)

A substrate with a transparent coating film (RA-2) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (RP-2) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

COMPARATIVE EXAMPLE 3 Preparation of Silica-Based Particles (RP-3)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 2310 grams of aqueous solution of sodium silicatewith concentration of 1.5 wt % when calculated as that of SiO₂ and 60grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as that of Al₂O₃ were added to obtain a dispersionliquid of SiO₂.Al₂O₃ primary particles (average diameter: 35 nm). TheMO_(x)/SiO₂ molar ratio (A) then was 0.005, and the pH of the reactionliquid was 12.0.

Next, 6980 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 135 gramsof aqueous solution of sodium aluminate with concentration of 0.5 wt %when calculated as Al₂O₃ were added to obtain a dispersion liquid ofcomposite oxide particles (RP3) (secondary particles) (average diameter:50 nm). The MO_(x)/SiO₂ molar ratio (B) then was 0.0038, and the pH ofthe reaction liquid was 12.0.

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (RP3) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(RP-3-1) with solid-phase concentration of 20 wt %.

Next, ammonia water was added to the aqueous dispersion liquid ofsilica-based particles (RP-3-1) to adjust the pH of the dispersionliquid to be 10.5. Then, the dispersion liquid was aged at 150° C. for11 hours, and was cooled to the room temperature. Then, the dispersionliquid was ion-exchanged for 3 hours using 400 grams of cation exchangeresin (Mitsubishi Kagaku K.K.: Diaion SK1B), and ion-exchanged for 3hours using 200 g of anion exchange resin (Mitsubishi Kagaku K.K.:Diaion SA20A), and ion-exchanged at 80° C. for 3 hours using 200 g ofcation exchange resin (Mitsubishi Kagaku K.K.: Diaion SK1B), to obtainan aqueous dispersion liquid of silica-based particles (RP-3-2) of solidcontent of 20 wt %. At that time, Na₂O and NH₃ content per silica-basedparticle in the aqueous dispersion liquid of silica-based particles(RP-3-2) were 12 ppm and 1000 ppm respectively.

Next, again, the dispersion liquid of silica-based particles (RP-3-2)was processed hydrothermally at 150° C. for 11 hours and cooled to theroom temperature. The dispersion liquid was ion-exchanged for 3 hoursusing 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.: DiaionSK1B), and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B) to obtain an aqueous dispersion liquid of silica-basedparticles (RP-3-3) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the dispersion liquid ofsilica-based particles (RP-3-3) were 1 ppm and 800 ppm respectively.

Next, an alcohol dispersion liquid of silica-based particles (RP-3) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (RA-3)

A substrate with a transparent coating film (RA-3) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (RP-3) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

COMPARATIVE EXAMPLE 4 Preparation of Silica-Based Particles (RP-4-1)

A mixture of 100 grams of silica-alumina sol (USBB-120, produced byCatalysts & Chemicals Industries Co., Ltd., average diameter: 25 nm,concentration of SiO₂.Al₂O₃: 20 wt %, Al₂O₃ content: 27 wt % in solidphase) and 3900 grams of pure water was heated to 98° C. While thistemperature was kept, 245 grams of aqueous solution of sodium silicatewith concentration of 1.5 wt % when calculated as that of SiO₂ and 6250grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as that of Al₂O₃ were added to obtain a dispersionliquid of SiO₂.Al₂O₃ primary particles (average diameter: 35 nm). TheMO_(x)/SiO₂ molar ratio (A) then was 5, and the pH of the reactionliquid was 12.0.

Next, 740 grams of aqueous solution of sodium silicate withconcentration of 1.5 wt % when calculated as that of SiO₂ and 18,860grams of aqueous solution of sodium aluminate with concentration of 0.5wt % when calculated as Al₂O₃ were added to obtain a dispersion liquidof composite oxide particles (RP4) (secondary particles) (averagediameter: 50 nm). The MO_(x)/SiO₂ molar ratio (B) then was 5, and the pHof the reaction liquid was 12.0.

Next, 1125 grams of pure water was added to 500 grams of dispersionliquid of the composite oxide particles (RP4) with solid-phaseconcentration of 13 wt % after cleaned with an ultrafiltration membrane.Drops of concentrated hydrochloric acid (concentration: 35.5 wt %) wereadded so as to set the pH to 1.0 to be dealuminated. Next, while 10 L ofhydrochloric acid solution with pH3 and 5 L of pure water were added,aluminate dissolved with the ultrafiltration membrane was separated andcleaned to obtain an aqueous dispersion liquid of silica-based particles(R-4-1) with solid-phase concentration of 20 wt %. At that time, Na₂Oand NH₃ content per silica-based particle in the aqueous dispersionliquid of silica-based particles (RP-4-1) were 1200 ppm and less than 10ppm respectively.

When the average diameter of the silica-based particles (RP-4-1) wasmeasured, it was approximately 5 nm. And when the silica-based particles(RP-1) were observed by taking transmission electron microscope (TEM),fine particles hardly have void. No substrate having transparent coatingfilm was manufactured.

COMPARATIVE EXAMPLE 5 Preparation of Silica-Based Particles (RP-5)

In the same method in example 1, the aqueous dispersion liquid ofsilica-based particles (P-1-1) with solid-phase concentration of 20 wt%.

Next, the dispersion liquid was ion-exchanged for 3 hours using 400grams of cation exchange resin (Mitsubishi Kagaku K.K.: Diaion SK1B),and ion-exchanged for 3 hours using 200 g of anion exchange resin(Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchanged at 80° C. for3 hours using 200 g of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), to obtain an aqueous dispersion liquid of silica-basedparticles (RP-5-2) of solid content of 20 wt %. At that time, Na₂O andNH₃ content per silica-based particle in the aqueous dispersion liquidof silica-based particles (RP-5-2) were 8 ppm and 1300 ppm respectively.

Next, an alcohol dispersion liquid of silica-based particles (RP-5) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (RA-5)

A substrate with a transparent coating film (RA-5) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (RP-5) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

COMPARATIVE EXAMPLE 6 Preparation of Silica-Based Particles (RP-6)

In the same method in example 1, the aqueous dispersion liquid ofsilica-based particles (P-1-1) having a silica-coating layer with solidcontent of 20 wt %. Next, the dispersion liquid was ion-exchanged for 3hours using 400 grams of cation exchange resin (Mitsubishi Kagaku K.K.:Diaion SK1B), and ion-exchanged for 3 hours using 200 g of anionexchange resin (Mitsubishi Kagaku K.K.: Diaion SA20A), and ion-exchangedat 80° C. for 3 hours using 200 g of cation exchange resin (MitsubishiKagaku K.K.: Diaion SK1B), to obtain an aqueous dispersion liquid ofsilica-based particles (RP-6-2) of solid content of 20% wt %. At thattime, Na₂O and NH₃ content per silica-based particle in the aqueousdispersion liquid of silica-based particles (RP-6-2) were 9 ppm and 1400ppm respectively.

Next, an alcohol dispersion liquid of silica-based particles (RP-6) withsolid content of 20 wt % was prepared, after ethanol was substituted forthe solvent using an ultrafiltration membrane.

Preparing a Substrate with a Transparent Coating Film (RA-6)

A substrate with a transparent coating film (RA-6) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (RP-6) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1).

COMPARATIVE EXAMPLE 7 Preparation of Silica-Based Particles (RP-7)

An alcoholic dispersion liquid of silica particles (RP-7) having solidcontent concentration of 20 wt % was prepared by substituting ethylalcohol with an ultrafiltration membrane for the solvent of silica sol(SI-45P, produced by Catalysts & Chemicals Industries Co., Ltd., averagediameter: 45 nm, refractive index: 1.43, concentration of SiO₂: 40 wt%).

Preparing a Substrate with a Transparent Coating Film (RA-7)

A substrate with a transparent coating film (RA-7) was prepared in thesame method as described in example 1 except that the alcohol dispersionliquid of the silica-based particles (RP-7) was substituted for thealcohol dispersion liquid of the silica-based particles (P-1). TABLE 1Preparation of silica-based fine particles Primary Particle SecondaryParticle Molar Average Molar Average Step (C) Hydro Ratio diameter Ratiodiameter Electrolyte Ratio Ratio Electrolyte Thermal (A) (Dp1) nm (B)(Dp2)nm (ME/MS) (B/A) (Dp1/Dp2) (ME/MS) Aging Process Example 1 0.2 280.07 40 — 0.35 0.7 — Yes Yes Example 2 0.2 35 0.07 50 — 0.35 0.7 — YesYes Example 3 0.2 120 0.07 171 — 0.35 0.7 — Yes Yes Example 4 0.2 350.15 50 0.5 0.75 0.7 0.004 Yes Yes Example 5 0.2 35 0.07 50 1.0 0.35 0.70.004 Yes Yes Example 6 0.2 35 0.07 50 1.0 0.35 0.7 0.004 Yes No Example7 0.2 35 0.03 50 1.0 0.15 0.7 0.004 Yes Yes Example 8 0.2 35 0.07 50 1.00.35 0.7 Yes Yes Yes Example 9 0.2 35 0.07 78 1.0 0.35 0.45 — Yes YesExample 10 0.2 35 0.07 37 1.0 0.35 0.96 — Yes Yes Example 11 0.2 10 0.0714 — 0.35 0.7 — Yes Yes Example 12 0.2 35 0.07 50 1.0 0.35 0.7 Yes YesNo Comp. Ex. 1 0.2 35 0.2 50 — 1 0.7 No No No Comp. Ex. 2 0.03 35 0.0350 — 1 0.7 No Yes Yes Comp. Ex. 3 0.005 35 0.0038 50 — 0.75 0.7 No YesYes Comp. Ex. 4 5 35 5 50 — 1 0.7 No No No Comp. Ex. 5 0.2 28 0.07 40 —0.35 0.7 No No No Comp. Ex. 6 0.2 28 0.07 40 — 0.35 0.7 No No No Comp.Ex. 7 — — — 45 — — — — — No

TABLE 2 Silica-based fine particles Molar Average Thickness Ratiodiameter S_(B) S_(C) of Outer Refractive Na₂O NH₃ Water (A) nm m²/g m²/gS_(B)/S_(C) Shell Index ppm ppm Resistance Example 1 0.0017 56 125 48.72.6 10 1.32 0.5 800 ◯ Example 2 0.0018 66 115 41.3 2.8 10 128 0.4 600 ⊚Example 3 0.0018 187 45 14.6 3.1 10 1.30 0.4 600 ◯ Example 4 0.0019 66118 41.3 2.9 10 1.26 0.3 700 ◯ Example 5 0.0015 66 111 41.3 2.7 10 1.320.5 600 ◯ Example 6 0.0017 66 120 41.3 2.9 10 1.29 0.8 1200 ◯ Example 70.0013 55 128 49.6 2.6 10 1.31 0.9 700 ◯ Example 8 0.0018 50 98 54.5 1.810 1.34 1.0 700 ◯ Example 9 0.0019 94 86 29.0 3.0 10 1.18 0.8 800 ◯Example 10 0.0017 53 129 51.5 2.5 10 1.33 0.8 700 ◯ Example 11 0.0020 14580 194.8 3.0 10 1.38 0.9 1000 ◯ Example 12 0.0018 60 69 45.5 1.5 111.32 0.8 800 ◯ Comp. Ex. 1 0.0017 5(collapse) — 545.5 — — — 1000 <10 —Comp. Ex. 2 0.0009 50 75 54.5 1.4 — 1.41 0.5 900 ◯ Comp. Ex. 3 0.0006 5073 54.5 1.3 — 1.42 0.5 800 ◯ Comp. Ex. 4 0.002 5(collapse) — 545.5 — — —1200 <10 — Comp. Ex. 5 0.0015 50 780 54.5 14.3 8 1.39 8 1300 X Comp. Ex.6 0.0020 66 214 41.3 5.2 10 1.39 9 1400 X Comp. Ex. 7 — 45 63 60.6 1.04— 1.43 4000 <10 ⊚

TABLE 3 Substrate with Transparent Coating Film Total Refractive PencilTransmittance % Haze % Reflectance % Index Adhesiveness Hardness Example1 96.3 0.3 0.6 1.36 ⊚ 4H Example 2 96.5 0.2 0.4 1.31 ⊚ 3H Example 3 96.10.3 0.5 1.32 ⊚ 3H Example 4 96.5 0.2 0.5 1.31 ⊚ 3H Example 5 96.3 0.20.6 1.35 ⊚ 3H Example 6 96.2 0.3 0.5 1.32 ◯ H Example 7 96.4 0.2 0.51.31 ⊚ 3H Example 8 96.1 0.3 0.5 1.31 ⊚ 3H Example 9 96.3 0.3 0.3 1.39 ⊚3H Example 10 96.1 0.3 0.6 1.30 ⊚ 3H Example 11 96.1 0.3 0.8 1.38 ⊚ 3HExample 12 96.2 0.2 0.6 1.31 ⊚ 3H Comp. Ex. 1 — — — — — — Comp. Ex. 296.3 0.3 1.5 1.45 ⊚ 3H Comp. Ex. 3 96.1 0.3 1.7 1.45 ⊚ 3H Comp. Ex. 4 —— — — — — Comp. Ex. 5 96.2 0.3 1.5 1.45 ◯ 3H Comp. Ex. 6 96.3 0.3 1.51.45 ◯ 3H Comp. Ex. 7 96.3 0.3 2.0 1.45 ⊚ 3H

1. A method of producing silica-based particles comprising the steps(a), (b), (c) and (e): (a) a step in which, when a dispersion liquid ofcomposite oxide particles is prepared by simultaneously adding anaqueous silicate solution and/or an acidic silicic acid solution and anaqueous solution of an alkali-soluble inorganic compound in an alkaliaqueous solution or in an alkali aqueous solution with seed particlesdispersed therein, if required, the aqueous silicate solution and/or theacidic silicic acid solution and the aqueous solution of alkali-solubleinorganic compound are added so that the molar ratio of MO_(x)/SiO₂ arein a range from 0.01 to 2, herein MO_(x) denoting an inorganic oxideother than silica and SiO₂ denoting silica to prepare the dispersionliquid of composite oxide particles with an average diameter (D_(p1)) ina range from 3 to 300 nm, (b) a step in which the aqueous silicatesolution and/or the acidic silicic acid solution and the aqueoussolution of alkali-soluble inorganic compound are added at the molarratio MO_(x)/SiO₂ smaller than that employed in the step (a) above toprepare a dispersion liquid of the composite oxide particles with theaverage diameters (D_(p2)) of up to 500 nm, (c) a step in which an acidis added to the dispersion liquid of composite oxide particles and thenat least a portion of elements constituting the composite oxideparticles other than silicon is removed to prepare a dispersion liquidof silica-based particles, and (e) a step in which cleaning is performedaccording to the necessity, and the dispersion liquid of silica-basedparticles is aged at a range from the room temperature to 300° C.
 2. Themethod of producing silica-based particles according to claim 1, whereina value of B/A (A: the molar ratio MO_(x)/SiO₂ in step (a), B: the molarratio MO_(x)/SiO₂ in step (b)) is 0.8 or below.
 3. The method ofproducing silica-based particles according to claim 1, wherein a ratio(D_(p1)/D_(p2)) of the average diameter (D_(p1)) of the composite oxideparticles versus the average diameter (D_(p2)) of the composite oxideparticles is in the range from 0.4 to 0.98.
 4. The method of producingsilica-based particles according to claim 1, wherein the step (b) and/orthe step (c) above are performed in the presence of an electrolytic saltat a molar ratio (M_(E)/M_(S)) of 10 or below in which M_(E) denotes amole number of the electrolytic salt and M_(S) denotes a mole number ofSiO₂.
 5. The method of producing silica-based particles according toclaim 1 further comprising a step (d) performed between the step (c) andthe step (e): (d) a step in which an organic silicon compound expressedby the following chemical formula (1) and/or a partially hydrolyzedproduct thereof, and an alkali aqueous solution, if necessary, are addedin the dispersion liquid of silica-based particles obtained in the step(c) above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1) wherein R denotes a not-substituted or substitutedhydrocarbon group having 1 to 10 carbon atoms, an acrylic group, anepoxy group, a methacrylic group, amino group, or a CF₂ group; X denotesan alkoxy group having 1 to 4 carbon atoms, a silanol group, a halogenor hydrogen; and n indicates an integral number in the range from 0 to3.
 6. The method of producing silica-based particles according to claim1 further comprising a step (f): (f) a step in which an organic siliconcompound expressed by the following chemical formula (1) and/or apartially hydrolyzed product thereof, and an alkali aqueous solution, ifnecessary, are added in the dispersion liquid of silica-based particlesobtained in the step (e) above to form a silica-coating layer on theparticles:R_(n)SiX_((4-n))  (1) wherein R denotes a not-substituted or substitutedhydrocarbon group having 1 to 10 carbon atoms, an acrylic group, anepoxy group, a methacrylic group, amino group, or a CF₂ group; X denotesan alkoxy group having 1 to 4 carbon atoms, a silanol group, a halogenor hydrogen; and n indicates an integral number in the range from 0 to3.
 7. The method of producing silica-based particles according to claim1, wherein pH of the alkali aqueous solution or of the alkali aqueoussolution with seed particles dispersed therein is 10 or more.
 8. Themethod of producing silica-based particles according to claim 1 furthercomprising a step (g) after the step (e) or the step (f): (g) a step inwhich cleaning is performed according to the necessity, and thenhydrothermal processing is performed at a temperature in the range from50 to 300° C.
 9. The method of producing silica-based particlesaccording to claim 1 further comprising a step (h) after the step (g):(h) a step in which the organic silicon compound expressed by thefollowing chemical formula (1) and/or a partially hydrolyzed productthereof, and an alkali aqueous solution, if necessary, are added in thedispersion liquid of silica-based particles obtained in the step (g)above to form a silica-coating layer on the particles:R_(n)SiX_((4-n))  (1) wherein R denotes a not-substituted or substitutedhydrocarbon group having 1 to 10 carbon atoms, an acrylic group, anepoxy group, a methacrylic group, amino group, or a CF₂ group; X denotesan alkoxy group having 1 to 4 carbon atoms, a silanol group, a halogenor hydrogen; and n indicates an integral number in the range from 0 to3.
 10. The method of producing silica-based particles according to claim1, wherein the hydrothermal processing is repeated several times. 11.The method of producing silica-based particles according to claim 1,wherein the inorganic oxide other than silica is alumina.
 12. A methodof producing silica-based particles further comprising: a step in whichthe dispersion liquid of silica-based particles obtained by the methodaccording to claim 1 is cleaned, dried, and calcinated, if required. 13.The method of producing silica-based particles according to claim 1,wherein an average diameter of the particles is in the range from 5 to500 nm.
 14. The method of producing silica-based particles according toclaim 1, wherein a content of an alkali metal oxide in the silica-basedparticles or the dispersion liquid of the silica-based particles is 5ppm or below as expressed by a content of M₂O per silica-based particle(M: an alkali metal element).
 15. The method of producing silica-basedparticles according to any of claim 1, wherein contents of ammoniaand/or ammonium ions in the silica-based particles or the dispersionliquid of the silica-based particles is 1500 ppm or below as expressedby a content of NH₃.
 16. Silica-based particles having a porous materialand/or cavities in an outer shell thereof, wherein a ratio (S_(B)/S_(C))of a specific surface area (S_(B)) of the particles measured by the BETmethod versus a specific surface area (S_(C)) expressed by the followingexpression is in the range from 1.1 to 5:S _(c)(m²/g)=6000/Dp(nm)*ρ Dp denoting an average diameter of thesilica-based particles, and ρ denoting a density (g/ml).
 17. Thesilica-based particles according to claim 16, wherein the averagediameter is in the range from 5 to 500 nm.
 18. The silica-basedparticles according to claim 16, wherein a thickness of the outer shellis in the range from 5 to 20 nm.
 19. The silica-based particlesaccording to claim 16, wherein the refractive index is in the range from1.15 to 1.38.
 20. A paint for forming coating film comprising: thesilica-based particles obtained by the production method according toclaim 1, or the silica-based particles according to claim 16; and amatrix for forming a coating film.
 21. The paint for forming coatingfilm according to claim 20 further comprising: oxide-based particlesother than the silica-based particles.
 22. A coated substrate having acoating film containing the silica-based particles produced by theproduction method according to claim 1 or the silica-based particlesaccording to claim 16 and a matrix for forming a coating film formedsingly or together with other coating film on a surface thereof.